• Journal of Elementary Mathematics Education in Korea
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• v.17 no.3
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• pp.457-481
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• 2013

Since the importance of teacher knowledge in teaching mathematics has been emphasized, there have been many studies exploring the nature or characteristics of such knowledge. However, there has been lack of research on the tools of investigating teacher knowledge. Given this background, this study explored teachers' knowledge of fraction lessons using classroom video analysis. The analyses of this study showed that knowledge of teaching methods was activated better than that of student thinking or mathematical content. Knowledge of fraction operation was activated better than that of fraction concept. The degree by which teacher knowledge was activated depended on the characteristics of the video clips used in the study. This paper raised some issues about teachers' knowledge of fraction lessons and suggested classroom video analysis as an alternative tool to measure teacher knowledge in the Korean context.

• The Mathematical Education
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• v.58 no.1
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• pp.121-138
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• 2019

The purpose of this study was to analyze the trends of domestic research on mathematics teacher education in terms of the period, topics, methods, subjects, and mathematics content strands. For this purpose, a total of 220 research articles dealing with mathematics teacher education were analyzed, which have been published since 2000 by the Korean Society of Mathematics Education in the three journals: (a) The Mathematical Education; (b) Education of Primary School Mathematics; and (c) Communications of Mathematical Education. Regarding the period when the research was conducted, the number of articles on mathematics teacher education has been rapidly increased since the late 2000s. Regarding the topics, research on teacher orientation has been the most frequent topic and the studies dealing with professional development for teachers, teaching practices, or teacher knowledge tend to be popular. Regarding methods, survey and case study have been most frequently employed in studying mathematics teacher education. Regarding subjects, the main participants were in-service teachers, pre-service teachers, elementary school teachers, and secondary school teachers, respectively, who were in charge of a regular class. Finally, regarding mathematics content strands, previous studies on mathematics teacher education were not specific to mathematics content strands. Given these results, this paper closes with important implications for future research directions on mathematics teacher education in Korea.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.1
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• pp.1-25
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• 2008

The purpose of this study was to identify pre-service teachers' Pedagogical Content Knowledge (PCK) about decimal calculation. A written questionnaire was developed dealing with decimal calculation. A total of 152 pre-service teachers from 3 universities were selected for this study; they had taken an elementary mathematics teaching method course and had no teaching experience. The results were as follows: First, with regard to the method of decimal calculation, most pre-service teachers were familiar with algorithms introduced in the textbook. But with regard to the meaning of decimal calculations, they had difficulties in understanding decimal multiplication or decimal division with decimal number. Second, pre-service teachers recognized reasons of errors as well as errors patterns that student might make. But this recognition was limited mainly to errors related to natural number calculation. Third, pre-service teachers frequently commented about decimals algorithms, picture models, the meanings of decimal calculations, and connections to natural number calculations. Many of them represented the meanings of decimal calculations through picture models as to help students' understanding, while they just mentioned algorithms or treated decimal calculation as natural number calculations with decimal point.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.397-413
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• 2010

On the standards or elements of teaching evaluation, the Korea Institute of Curriculum and Evaluation(KICE) has carried out the following research such as : 1) development of the standards on teaching evaluation between 2004 and 2006, and 2) investigation on the elements of Pedagogical Content Knowledge including understanding of learners between 2007 and 2008. The purposes of development of mathematics teaching evaluation standards through those studies were to improve not only mathematics teachers' professionalism but also their own teaching methods or strategies. In this study, the standards were revised and modified by analyzing the results of those studies (namely, evaluation standards) focused on the knowledge of teaching contexts. For this purpose, application of instructional tools and materials, commercial manipulatives, environment of classroom including distribution and control of class group, atmosphere of classroom, management of teaching contexts including management of student were re-established based on the results of the search mentioned above. According to those evaluation domains, elements on teaching evaluation focused on the knowledge of teaching contexts were established.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.71-84
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• 2012

The purpose of this study is to analyze some Korean elementary pre-service teachers' Mathematical Knowledge for Teaching(MKT) and compare the results with those obtained by Kwon, Nam, & Kim(2009), so that we can provide some suggestions to improve education of elementary mathematics subject at Korean teachers colleges. For this purpose, we selected the MKT items on number and operations which were adapted for Korean in-service teachers by Kwon et al. The survey consisting of those items was administered to 88 Korean elementary pre-service teachers at teachers college, J University. The results are the following: First, the respondents, elementary pre-service teachers, showed that they already had a sufficient amount of Content Knowledge(CK) on number and operations, but that their level of Knowledge of Content and Students(KCS) was insufficient. This means we need to strengthen our students' KCS in education of elementary mathematics subject at our teachers colleges. Second, there was a strong correlation, in both CK and KCS, of item difficulty felt by the respondents with that by the Kwon et al's in-service teachers. Third, although the respondents valued the MKT items more than the above-mentioned elementary in-service teachers, about 70% of them said the items were never learned at their college. Furthermore, they had different opinions on some of the items from their counterparts'. The suggestions we get here are we need to first consider the results in improving education of elementary mathematics subject at our teachers colleges and second develop MKT items suitable for the situation of Korean schools and curriculums in order to obtain exact estimations of Korean elementary pre-service teachers' MKT.

• The Mathematical Education
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• v.60 no.3
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• pp.297-319
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• 2021

The present study explored a relationship between mathematical understandings of teachers and ways in which their knowledge transferred in designing lessons for hypothetical students from Gess-Newsome (1999)'s transformative perspective of pedagogical content knowledge. To this end, we conducted clinical interviews with four secondary mathematics teachers of their solving and teaching of equation writing. After analyzing the teacher participants' attention to Key Developmental Understandings (Simon, 2007) in solving equation writing, we sought to understand the relationship between their mathematical knowledge of the problems and mathematical knowledge in teaching the problems to hypothetical students. Two of the four teachers who attended the key developmental understandings solved the problems more successfully than those who did not. The other two teachers had trouble representing and explaining the problems, which involved reasoning with improper fractions or reciprocal relationships between quantities. The key developmental understandings of all four teachers were reflected in their pedagogical actions for teaching the equation writing problems. The findings contribute to teacher education by providing empirical data on the relationship between teachers' mathematical knowledge and their knowledge for teaching particular mathematics.

• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.179-193
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• 2006

The aim of this paper is to explore and understand, using in-depth interviews, the participant's enthusiasm for and involvement in studying mathematics and the deeper nature of his/her interest in mathematics teaching. In addition a larger aim is to understand how the individual's interest in mathematics and teaching are linked to his/her larger personal fulfillment. We conducted in-depth interviews with 4 pre-service teachers' subjective experiences focusing on deep motivation, pedagogical content knowledge, inner vision. Interviews focus much more on the participant's spontaneous feeling, consciousness, and state as these arise in the interview, and on past foiling, consciousness and state as they appear to the participant subjectively retrospectively in his/her memory. The output of this research consists of 2 portraits out of 4 individual participants, highlighting and conceptually developing the specific aspects under study; different ways in which individuals' involvement with the subject area affects their motivation, inner visions and academic efforts toward becoming teachers. Larger aspects of pre-service teachers' subjective experiences were sketched by contrasting the two cases. Several suggestions were put at the end to enhance mathematics education concerning curriculum development.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.109-135
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• 2012

On the standards or elements of teaching evaluation, the Korea Institute of Curriculum and Evaluation(KICE) has carried out the following research such as : 1) development of the standards on teaching evaluation between 2004 and 2006, and 2) investigation on the elements of Teacher Knowledge. The purposes of development of evaluation standards for mathematics teaching through those studies were to improve not only mathematics teachers' professionalism but also their own teaching methods or strategies. In this study, the standards were revised and modified by analyzing the results of those studies focused on the knowledge of subject matter knowledge, knowledge of learners' understanding, teaching and learning methods and assessments, and teaching contexts. For this purpose, the part of subject matter knowledge was consisted of four evaluation domains such as the knowledge of curriculum reconstruction, knowledge of mathematical contents, methodological knowledge, mathematical value. The part of Learners' unders tanding included the evaluation domains such as students' intellectual and achievement level, students' misconception in math, students' motivation on learning, students' attitude on mathematics learning, and students' learning strategies. The part of teaching methods and evaluation was consisted of seventh evaluation domains such as instruction involving instructional goal and content, instruction involving problem-solving activity, instruction involving learners' achievement level and attitude, instruction on communication skills, planning of assessment method and procedure, development on assessment tool, application on assessment result in class were new established. Also, the part of teaching context was consisted of four evaluation domains such as application of instructional tools and materials, commercial manipulatives, environment of classroom including distribution and control of class group, atmosphere of classroom, management of teaching contexts including management of student. According to those evaluation domains of each teacher knowledge, elements on teaching evaluation focused on the teacher's knowledge were established using the instructional evaluation framework, which is developed in this study, including the four areas of obtaining, planning, acting, and reflecting.

• Communications of Mathematical Education
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• v.25 no.4
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• pp.693-734
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• 2011

The purpose of this research is to analyze the pedagogical content knowledge on the natural number concepts of Korean Elementary School Teachers. Shulman(1986b) had developed a tool in order to understand teachers' knowledge, as he defined three types of knowledge in teaching ; Subject Matter Knowledge, Curricular Knowledge, and Pedagogical Content Knowledge. Pang(2002) defined two types of elements including in the ways of teaching ; individual element, and sociocultural element. Two research questions are addressed; (1) What is the pedagogical content knowledge of Natural number Concepts for Korean Elementary School Teachers? ; (2) What factors are included in the pedagogical content knowledge of Natural number Concepts for Korean Elementary School Teachers? Findings reveal that (1) the Korean Elementary School Teachers had three types of the pedagogical content knowledge on the natural number concepts; (2) Teacher Factors were more included than Social-Cultural Factors in the pedagogical content knowledge on the natural number concepts of the Korean Elementary School Teachers. Further suggestions were made for future researches to include (1) a comparative study on teachers between ordinary teachers and those who majored mathematics education in the graduate school. (2) an analysis on the classroom activities about the natural number concepts.

• School Mathematics
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• v.17 no.3
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• pp.407-421
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• 2015

Linear system is a basic subject matter of school mathematics courses. Even though elimination is a useful method to solve linear systems, its fundamental principles were not discussed pedagogically. The purpose of this study is to help the development of mathematical content knowledge on linear systems conceptions. To do this, various representations and translations among them were considered, and in particular, the basic principles for elimination method are analyzed geometrically. Rectangular representation is used to solve word problem treated in numbers of things in elementary mathematics and it is useful as a pre-stage to introduce elimination. Slopes and intercepts of lines associated linear equations are used to obtain the Cramer's formula and this solving method was showing the connection between algebraic and geometric procedures. Strategy deleting variables of linear systems by elementary operations is explored and associated with the movements of lines in the family of lines passing through a fixed point. The development of mathematical content knowledge is expected to enhance pedagogical content knowledges.